Blunt ending (T4) + BAP + Ligation in the same buffer??

Hey guys I was wondering if anybody has attempted to blunt end a vector using T4 polymerase, dephosphorylate using BAP then ligate a fragment all in the same original T4 buffer of course inactivating each enzyme after each step. This way I won't have to loose much DNA compared to purifying after each stage.

The problem with this is that Blunting with T4 pol requires dNTPs, even if you are chewing back a 3' overhang (they are needed to prevent overchewing). Even if you inactivate the T4 pol, all the dNTPs will still be hanging around and they will be dead end substrates for your phosphatase, reducing the dephosphorylation efficiency. I do this all the time and I just use a PCR clean up column (qiagen) after the blunting step, but I don't repurify after phosphatase treatment.

I would add that gel purifying your cut vector BEFORE doing all of this actually does help in decreasing vector background on you ligations.